This was proved by Donoho and Tanner [1]}. (In their terminology, \(D_N={\sf A}{\mathbb {R}}^N_+\) , where \({\sf A}\)  is the random matrix with columns \(X_1,\dots ,X_N\)  and \({\mathbb {R}}^N_+\)  is the nonnegative orthant of \({\mathbb {R}}^N\) .)
